cohesion model adaptive

Purpose

Modelling powder cohesion as proposed by Obermayr et al..

Syntax

cohesion adaptive settings keyword values

initialize_cohesion values = 'on' or 'off'
  on = cohesive stress is initialized to initialCohesiveStress.
  off = cohesive stress is initialized to zero for non-restarted runs and to the values stored in restart files otherwise . This is the default setting.
compatibilityVersion = version_number
  version_number < 6.3.2 = use legacy implementation that uses 
  version_number >= 6.3.2 = use  [default, set explicitly to disable warning]

Associated material properties

Material interaction properties

initialCohesiveStress ( $\sigma_0$ ): initial cohesive stress between two materials [Pa]
maxCohesiveStress ( $\sigma_{max}$ ): maximum cohesive stress between two materials [Pa]
cohesionStrength ( $k_c$ ): ratio between the cohesive force and the net normal force between two materials [ $\cdot$ ]

Description

The adaptive cohesion model creates a normal force between two particles in contact based on the following relation:

$F_c = \pi r_{eff}^2 \max(\sigma_{c}, \sigma_{c}^{old})$

where $r_{eff} = 2 r_i r_j/(r_i+r_j)$ is the effective radius (for spheres), $\sigma_{c}$ is the current cohesion stress and $\sigma_{c}^{old}$ is the cohesion stress calculated at the previous time-step. In case of sphere-wall interactions, the effective radius is calculated by considering the wall as a sphere of infinite radius; hence, $r_{eff} = 2 r$ . Non-spherical particles use a $r_{eff}$ that is defined according to the particle shape. If a new contact between two particles is established at the current time-step, then $\sigma_{c}^{old}$ is initialized to zero. If the contact between two particles is broken (i.e., they do not overlap anymore), then $\sigma_{c}^{old}$ is reset to zero.

The current cohesion stress is given by the relation:

$\sigma_{c} = \min(\tilde{F}_n k_c/(\pi r_{eff}^2),\sigma_{max})$

where $\tilde{F}_n = F_n - F_c$ , $F_n$ is the normal force calculated from the normal model. At time-step zero all particles in contact have a current cohesion stress equal to $\sigma_{0}$ .

Warning

From Aspherix 6.3.2 the implementation has been modified. While recent Aspherix versions use the implementation as given above (which matches the reference implementation from literature), older Aspherix versions use $\tilde{F}_n = F_n$ . For backward compatilibility, the legacy implementation can be enabled by setting compatibilityVersion 6.3.1 (a warning will be shown). Newer version might show a warning too, which can be disabled by explicitly defining compatibilityVersion 6.3.2 (or a more recent version number).

The keyword initialize_cohesion can be used to initialize the cohesive stresses of all contacts to the value of initialCohesiveStress. This is useful to set a defined initial cohesion value after e.g. creating a packing.

For further details about this model see the original paper by Obermayr et al.

Restrictions

Coarse-graining information:

Using coarsegraining in combination with this command might lead to different dynamics or system state and thus to inconsistencies.

Literature

[1] Obermayr et al. Journal of Terramechanics 53, 93-104 (2014).